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Publications and source records attributed to D. V. Ahluwalia.
This is first of the two invited lectures presented (by D. V. Ahluwalia) at the ``XVII International School of Theoretical Physics: Standard Model and Beyond' 93.'' The text is essentially based on a recent publication by the present authors [Phys. Lett. B 316 (1993) 102]. Here we show that the Dirac-like construct in the $(j,0)\oplus(0,j)$ representation space supports a Bargmann-Wightman-Wigner-type quantum field theory.
This is second of the two invited lectures presented (by D. V. Ahluwalia) at the ``XVII International School of Theoretical Physics: Standard Model and Beyond' 93.'' The text is essentially based on a recent publication by the present authors [Mod. Phys. Lett. A (in press)]. Here, after briefly reviewing the $(j,0)\oplus(0,j)$ Dirac-like construct in the front form, we present a detailed construction of the $(j,0)\oplus(0,j)$ Majorana-like fields.
By considering the parity-transformation properties of the $(1/2,\,0)$ and $(0,\,1/2)$ fields in the {\it front form} we find ourselves forced to study the front-form evolution both along $x^+$ and $x^-$ directions. As a by product, we find that half of the dynamical degrees of freedom of a full theory live on the $x^+=0$ surface and the other half on the $x^-=0$ surface. Elsewhere, Jacob shows how these results are required to build a satisfactory, and internally consistent, front-form quantum field theory.
This version corrects an inportant typographical error in Eq. 17. COMMENTS, FOR THE RECORD: A referees reoprt from Phys. Rev. Lett. read in part ``The first named author has appreciated my exceptionally long report. He has read and well assimilated the literature I suggested. Congratulations! This very new version of the manuscript has now three authors and carries a very well chosen title. Indeed Bargmann, Wightman and Wigner had studied, this subject forty years ago, in an unpublished book (several chapters were distributed as preprints). The authors explain well the scope of their paper. They have made a thorough construction of a field theory of a non usual Wigner type; that is completely new and all references are relevant. {\it This paper should be published.}" Despite the fact that no other report was received, the editors of Phys. Rev. Lett. rejected this paper. D.V.A.
Contrary to the usual belief, by carefully examining the operation of parity transformation on the $(1,0)\oplus(0,1)$ mesons in the generalized canonical representation, we establish that the $(j,0)\oplus(0,j)$ meson-antimeson pair have {\it opposite} intrinsic parity. This opens up the possibility that while the particles without an internal structure may utilize one representation of the Lorentz group, phenomenologies of composite particles may exploit a different representation. As such (perhaps, only some of) the meson structures beyond the standard $q\,\overline {Q}$ may exploit the $(j,0)\oplus(0,j)$ generalized canonical representation of the Lorentz group -- this would result in a meson and the associated antimeson to manifest themselves in {\it different} partial waves. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CONSTRUCTIVE COMMENTS WELCOME, AS ALWAYS D. V. A. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
On the one hand any effective action of the QCD, $S[π,\,ρ,\,ω,\ldots,N,\,\overline N,\,Δ^{3/2},\ldots]$, would involve, at least in principle, a tower of hadronic fields of all spins; on the other hand the front form of the field theory has emerged as an appropriate framework to investigate the high energy behaviour of many systems. Motivated by these simple considerations we present a systematic formalism which explicitly provides the front form fields appropriate for constructing a $S[π,\,ρ,\,ω,\ldots,N,\,\overline N,\,Δ^{3/2},\ldots]$. Further, a transformation matrix $Ω(j)$ is constructed which determines how the front form hadronic fields superimpose to yield the more familiar instant form fields. Explicit results for the front form hadronic fields up to spin two are catalogued in appendixes. For spin one half, the $Ω(1/2)$ coincides with the celebrated ``Melosh transformation.'' The formalism, without explicitly invoking any wave equations, reproduces spin one half front-form results of Lepage and Brodsky, and Dziembowski.